A004322 Binomial coefficient C(3n,n-4).

1, 15, 153, 1330, 10626, 80730, 593775, 4272048, 30260340, 211915132, 1471442973, 10150595910, 69668534468, 476260169700, 3245372870670, 22057981462440, 149608375854525, 1012974972473835, 6848956078664700, 46252743903616536, 312049055023946856, 2103535234151144200

Offset

4,2

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.

Links

Seiichi Manyama, Table of n, a(n) for n = 4..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Milan Janjić, Two Enumerative Functions.

Formula

D-finite with recurrence -2*(2*n+3)*(n+2)*(n-4)*a(n) + 3*n*(3*n-1)*(3*n-2)*a(n-1) = 0. - R. J. Mathar, Jan 13 2025

a(n) ~ 3^(3*n+1/2) / (2^(2*n+5) * sqrt(Pi*n)). - Amiram Eldar, Sep 06 2025

Mathematica

Table[Binomial[3*n, n - 4], {n, 4, 25}] (* Paolo Xausa, Jan 13 2025 *)

Crossrefs

Sequence in context: A206361 A041424 A021124 * A125403 A010035 A370765

Adjacent sequences: A004319 A004320 A004321 * A004323 A004324 A004325

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved